{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CW4DDOU24SLUYEIW7UYEXRWVXL","short_pith_number":"pith:CW4DDOU2","canonical_record":{"source":{"id":"1502.01774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T02:01:46Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"ec44926ca8ddf39e096477064365a5745d302c91e3037061347c103921f3e1cc","abstract_canon_sha256":"bbe618750f3a0d7629c0f15326d9744dee9215f000de9644af43159fff98c36a"},"schema_version":"1.0"},"canonical_sha256":"15b831ba9ae4974c1116fd304bc6d5bafd3fc863a867b3ad778cbc16f43747e9","source":{"kind":"arxiv","id":"1502.01774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01774","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01774v1","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01774","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"CW4DDOU24SLU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CW4DDOU24SLUYEIW","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CW4DDOU2","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CW4DDOU24SLUYEIW7UYEXRWVXL","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T02:01:46Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"ec44926ca8ddf39e096477064365a5745d302c91e3037061347c103921f3e1cc","abstract_canon_sha256":"bbe618750f3a0d7629c0f15326d9744dee9215f000de9644af43159fff98c36a"},"schema_version":"1.0"},"canonical_sha256":"15b831ba9ae4974c1116fd304bc6d5bafd3fc863a867b3ad778cbc16f43747e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:01.935783Z","signature_b64":"uUkW8NjvBuG4G+ri2S8/fwPqN/iwyGXVXRg3sRhta/lNe4YbuUTxQcqbeTlEWqZpw1on+5eyGyZh81sRtMVLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b831ba9ae4974c1116fd304bc6d5bafd3fc863a867b3ad778cbc16f43747e9","last_reissued_at":"2026-05-18T01:25:01.935169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:01.935169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01774","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTTqArZBXew7FyF/34OG+sL77L4oppYSrOaACklo7VMhRdifmjkvAM0S33UXgLzT21l+fF7r5El/oGjAtY66BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:15:17.802159Z"},"content_sha256":"95bd919d88512af4590caa94fe52398209221bcd728404ae6ae5560f7f49c4aa","schema_version":"1.0","event_id":"sha256:95bd919d88512af4590caa94fe52398209221bcd728404ae6ae5560f7f49c4aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CW4DDOU24SLUYEIW7UYEXRWVXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central Invariants of the Constrained KP Hierarchies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Si-Qi Liu, Xu Zhou, Youjin Zhang","submitted_at":"2015-02-06T02:01:46Z","abstract_excerpt":"We compute the central invariants of the bihamiltonian structures of the constrained KP hierarchies, and show that these integrable hierarchies are topological deformations of their hydrodynamic limits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01774","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtpwaSY9MJVsqj/J5oZclBJr/9CdDOfeABZZYsYmtj4lRLaXQp0/j7TNu+60wOtOV4ShNknIhdgCdnjuILhyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:15:17.802832Z"},"content_sha256":"2b1f1e97f752d838229742ac069c325133538cc266c6400934b6a651a9409645","schema_version":"1.0","event_id":"sha256:2b1f1e97f752d838229742ac069c325133538cc266c6400934b6a651a9409645"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CW4DDOU24SLUYEIW7UYEXRWVXL/bundle.json","state_url":"https://pith.science/pith/CW4DDOU24SLUYEIW7UYEXRWVXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CW4DDOU24SLUYEIW7UYEXRWVXL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T18:15:17Z","links":{"resolver":"https://pith.science/pith/CW4DDOU24SLUYEIW7UYEXRWVXL","bundle":"https://pith.science/pith/CW4DDOU24SLUYEIW7UYEXRWVXL/bundle.json","state":"https://pith.science/pith/CW4DDOU24SLUYEIW7UYEXRWVXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CW4DDOU24SLUYEIW7UYEXRWVXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CW4DDOU24SLUYEIW7UYEXRWVXL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bbe618750f3a0d7629c0f15326d9744dee9215f000de9644af43159fff98c36a","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T02:01:46Z","title_canon_sha256":"ec44926ca8ddf39e096477064365a5745d302c91e3037061347c103921f3e1cc"},"schema_version":"1.0","source":{"id":"1502.01774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01774","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01774v1","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01774","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"CW4DDOU24SLU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CW4DDOU24SLUYEIW","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CW4DDOU2","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:2b1f1e97f752d838229742ac069c325133538cc266c6400934b6a651a9409645","target":"graph","created_at":"2026-05-18T01:25:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We compute the central invariants of the bihamiltonian structures of the constrained KP hierarchies, and show that these integrable hierarchies are topological deformations of their hydrodynamic limits.","authors_text":"Si-Qi Liu, Xu Zhou, Youjin Zhang","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T02:01:46Z","title":"Central Invariants of the Constrained KP Hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01774","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:95bd919d88512af4590caa94fe52398209221bcd728404ae6ae5560f7f49c4aa","target":"record","created_at":"2026-05-18T01:25:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bbe618750f3a0d7629c0f15326d9744dee9215f000de9644af43159fff98c36a","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T02:01:46Z","title_canon_sha256":"ec44926ca8ddf39e096477064365a5745d302c91e3037061347c103921f3e1cc"},"schema_version":"1.0","source":{"id":"1502.01774","kind":"arxiv","version":1}},"canonical_sha256":"15b831ba9ae4974c1116fd304bc6d5bafd3fc863a867b3ad778cbc16f43747e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b831ba9ae4974c1116fd304bc6d5bafd3fc863a867b3ad778cbc16f43747e9","first_computed_at":"2026-05-18T01:25:01.935169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:01.935169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUkW8NjvBuG4G+ri2S8/fwPqN/iwyGXVXRg3sRhta/lNe4YbuUTxQcqbeTlEWqZpw1on+5eyGyZh81sRtMVLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:01.935783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95bd919d88512af4590caa94fe52398209221bcd728404ae6ae5560f7f49c4aa","sha256:2b1f1e97f752d838229742ac069c325133538cc266c6400934b6a651a9409645"],"state_sha256":"209e8d19b152f02e29620c6d0fcc4e79b55d4af0661de13b42ac773c05633880"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MlgXFvaBgFru+/s70BfXjRc3cgwn9eIa+Jk4if4Quez72vQDFAO5f1qTYV08IFK/fwZ4/mQw2CHZdFYj8qmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:15:17.806237Z","bundle_sha256":"a347a4e7481ed90a0877259603d99b8e1e5d6b79e92054eafd905ac65042b6ef"}}